So the short answer is "yes" but it's possible just like how it's possible for Taylor Swift to come bursting through my office door, proclaim her undying love for me and whisk me away.
It's possible, but not probable, and here's why...
1 - Storm-scale drawing: Sure we have the ability with remote sensing to see the approximate top of a storm, and we have the reported bottom, but those layers are constantly moving. That would require an immense amount of computing power to send out those renderings on a near constant basis. We would also probably need to integrate some kind of level 3 data where you can slice a storm to see the kind of precip - but aviation wx also has to take into account cloud cover and not just precip. We also have to acknowledge that radar is more incomplete the farther from the station you are, as shown below:
2. Need for streaming data - Goes without saying that we can't have all of these features without some kind of streaming data firehose
3. Screen clutter and performance - I don't see how we could make some kind of a quasi-real time wx drawing work on screen, except in 3D view, and even then it could crowd the busy screenspace. Plus, we'd have to factor in performance limitations for adding a new streaming layer on.
All in all, this is a really cool idea, but I just don't think it's feasible at the moment.